1. For the pipe wrench, there's some theoretical situations where a pipe wrench might be more useful to bring along than a mallet but they don't come up often enough to remotely justify it.
2. Yes, though it depends on what you're doing. The Pipe Wrench is pretty awesome, but if you know you'll mostly just be repairing or mostly just be rebuilding the mallet or spanner might be a better idea. Just like how a lot of gunners like to bring a mallet instead of a pipe wrench, you might prefer to take a mallet to quickly repair a heavy weapon you're on. Of course, you can eschew the fire extinguisher entirely in most of those cases and just go mallet/spanner/buff hammer, you're probably not the main engineer so it's probably not too risky to trade extinguishing for awesome repairs.
3. lolno. If you're on the helm something has gone horribly wrong. If you know that your pilot is going to ragequit or disconnect a lot MAYBE you'll want to bring something like hydrogen or moonshine so you won't be completely left in the dust, but it's generally better to trust your pilot to do his job. If he's off the helm repairing something and you're on the helm driving, you guys need to switch places.
4. That depends on what those enemy ships are doing. Generally your job will be to stay near the hull and wait for the first sign of burst damage, that peace and quiet will shatter very quickly and you'll only have a split second to repair the hull and stop it from taking permanent damage. If it's safe to do so, you should get on a third gun and help with damage, but you'll have to pay careful attention to your surroundings so that the hull won't instantly disappear, if there's a ship ready to shoot you assume it will shoot you. Generally if your pilot is keeping in the enemy's blind spot it's safe to shoot so long the enemy didn't bring asshwachas. It's risky, but that extra damage even if it's small can be utterly devastating. I've made great use of a flak/gat Pyra with a flamethrower on the side, by itself the flamethrower isn't worth much and it certainly isn't worth ignoring hull damage but that little extra cherry on top will GREATLY increase the speed at which we can kill just about any ship.